[Haskell] Computus (#679)

Author: jiegillet

contents/computus/code/haskell/gauss_easter.hs

@@ -0,0 +1,55 @@
+data Mode = Servois | Easter
+
+computus :: Mode -> Int -> String
+computus mode year =
+  case mode of
+    Servois ->
+      -- Value for Servois' table
+      show $ (21 + d) `mod` 31
+    Easter ->
+      -- Determination of the correct month for Easter
+      if 22 + d + f > 31
+        then "April " ++ show (d + f - 9)
+        else "March " ++ show (22 + d + f)
+  where
+    a, b, c, d, e, f, k, m, n, p, q :: Int
+    -- Year's position on the 19 year metonic cycle
+    a = year `mod` 19
+    -- Century index
+    k = year `div` 100
+    -- Shift of metonic cycle, add a day offset every 300 years
+    p = (13 + 8 * k) `div` 25
+    -- Correction for non-observed leap days
+    q = k `div` 4
+    -- Correction to starting point of calculation each century
+    m = (15 - p + k - q) `mod` 30
+    -- Number of days from March 21st until the full moon
+    d = (19 * a + m) `mod` 30
+    -- Finding the next Sunday
+    -- Century-based offset in weekly calculation
+    n = (4 + k - q) `mod` 7
+    -- Correction for leap days
+    b = year `mod` 4
+    c = year `mod` 7
+    -- Days from d to next Sunday
+    e = (2 * b + 4 * c + 6 * d + n) `mod` 7
+    -- Historical corrections for April 26 and 25
+    f =
+      if (d == 29 && e == 6) || (d == 28 && e == 6 && a > 10)
+        then -1
+        else e
+
+-- Here, we will output the date of the Paschal full moon
+-- (using Servois notation), and Easter for 2020-2030
+main :: IO ()
+main = do
+  let years :: [Int]
+      years = [2020 .. 2030]
+      servoisNumbers, easterDates :: [String]
+      servoisNumbers = map (computus Servois) years
+      easterDates = map (computus Easter) years
+  putStrLn "The following are the dates of the Paschal full moon (using Servois notation) and the date of Easter for 2020-2030 AD:"
+  putStrLn "Year\tServois number\tEaster"
+  let conc :: Int -> String -> String -> String
+      conc y s e = show y ++ "\t" ++ s ++ "\t\t" ++ e
+  mapM_ putStrLn $ zipWith3 conc years servoisNumbers easterDates

contents/computus/computus.md

@@ -281,6 +281,8 @@ For now, we have the code outputting a tuple of $$d$$ and $$e$$, so users can us
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/gauss_easter.jl)
+{% sample lang="hs" %}
+[import, lang:"haskell"](code/haskell/gauss_easter.hs)
 {% sample lang="py" %}
 [import, lang:"python"](code/python/gauss_easter.py)
 {% sample lang="crystal" %}